The move will decide whether the famed Californian street venue remains an IndyCar weekend, or is opened up for a return by Formula 1.
The current deal expires in 2015.
Long Beach City Council's discussions revolve around an approach made to its mayor Bob Foster by Bernie Ecclestone last year about the prospect of an F1 event put together by Chris Pook, who founded the Long Beach race in 1975.
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The current contract is held by the Grand Prix Association of Long Beach, which is in the process of preparing for the 40th race on the streets of the southern Californian city next month.
Long Beach hosted seven F1 grands prix before the event was switched to CART, and later IndyCar.
Key to any possible F1 return is finances, with F1's sanction fee expected to be far in excess of the approximately $2 million demanded by IndyCar.
The venue would also require upgrades to both the track and surrounding facilities in order to reach F1 standard.
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